

A004104


Number of selfdual signed graphs with n nodes. Also number of selfcomplementary 2multigraphs on n nodes.
(Formerly M1649)


5



1, 1, 2, 6, 20, 86, 662, 8120, 171526, 5909259, 348089533, 33883250874, 5476590066777, 1490141905609371, 666003784522738152, 509204473666338077658, 636051958071749028811326, 1375164117171886868027357906, 4844133410739656724629165903483, 29777568550007746192195431057341474
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

A 2multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (selfloops are not allowed).
Of a(1) through a(22) only a(3) = 2 is prime.  Jonathan Vos Post, Feb 19 2011


REFERENCES

F. Harary and R. W. Robinson, Exposition of the enumeration of pointlinesigned graphs, pp. 19  33 of Proc. Second Caribbean Conference Combinatorics and Computing (Bridgetown, 1977). Ed. R. C. Read and C. C. Cadogan. University of the West Indies, Cave Hill Campus, Barbados, 1977. vii+223 pp.
R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50 (terms 1..22 from R. W. Robinson)
Frank Harary, Edgar M. Palmer, Robert W. Robinson, Allen J. Schwenk, Enumeration of graphs with signed points and lines, J. Graph Theory 1 (1977), no. 4, 295308.
R. W. Robinson, Notes  "A Present for Neil Sloane"
R. W. Robinson, Notes  computer printout


PROG

(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v) = {sum(i=2, #v, sum(j=1, i1, if(v[i]*v[j]%2==0, gcd(v[i], v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]\4*2))}
a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ Andrew Howroyd, Sep 16 2018


CROSSREFS

Cf. A004102, A052111, A052112, A052113.
Sequence in context: A177480 A089179 A177483 * A304932 A293032 A241497
Adjacent sequences: A004101 A004102 A004103 * A004105 A004106 A004107


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Vladeta Jovovic, Jan 19 2000
a(18)a(20) added by Andrew Howroyd, Sep 16 2018


STATUS

approved



